$A$ box $A$ contains $2$ white,$3$ red and $2$ black balls. Another box $B$ contains $4$ white,$2$ red and $3$ black balls. If two balls are drawn at random,without replacement,from a randomly selected box and one ball turns out to be white while the other ball turns out to be red,then the probability that both balls are drawn from box $B$ is

The contents of $3$ boxes are as follows. If one box is chosen at random and three balls are drawn from it and they are all of different colours,find the probability that they come from Box $2$.
Box $1$ contains $1$ black,$2$ white,$3$ red balls.
Box $2$ contains $1$ black,$1$ white,$2$ red balls.
Box $3$ contains $5$ black,$4$ white,$1$ red balls.

Bag $I$ contains $3$ red and $4$ black balls. Bag $II$ contains $5$ red and $6$ black balls. If one ball is drawn at random from one of the bags, and it is found to be red, then the probability that it was drawn from Bag $II$, is

One card is missing in a pack of $52$ playing cards. If two cards are drawn randomly from the remaining cards at a time and are found to be spades,then the probability that the missing card is not a spade is

$A$ diagnostic test has a probability of $0.95$ of giving a positive result when applied to a person suffering from a certain disease and a probability of $0.10$ of giving a positive result when given to a non-sufferer. It is estimated that $0.5 \%$ of the population are suffering from the disease. If this test is administered to a person from this population about whom there is no information relating to the incidence of this disease and the test gives a positive result, then the probability that the person is a sufferer is:

From a certain population, the probability of choosing a colour blind man is $\frac{1}{20}$ and that of a colour blind woman is $\frac{1}{10}$. If a randomly chosen person is found to be colour blind, then the probability that the person is a man is